UNCONVENTIONAL HAMILTON-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF REISSNER SANDWICH PLATE

According to the basic idea of classical yin-yang complementarity and modern dual-complementarity,in a simple and unified way proposed by Luo(1987),some uncon- ventional Hamilton-type variational principles for dynamics of Reissner sandwich plate can be established systematically.The unconventional Hamilton-type variation principle can fully characterize the initial-boundary-value problem of this dynamics.In this pa- per,an important integral relation is given,which can be considered as the generalized principle of virtual work in mechanics.Based on this relation,it is possible not only to obtain the principle of virtual work in dynamics of Reissner sandwich plate,but also to derive systematically the complementary functionals for five-field,two-field and one-field unconventional Hamilton-type variational principles by the generalized Legender trans- formations.Furthermore,with this approach,the intrinsic relationship among the various principles can be explained clearly.     

On the variational principles in linear elastodynamics

A new approach is proposed for the systematic derivation of varïous variational principles in linear elastodynamics. Based on an important integral relation in terms of convolutions given by the authors, the new approach can be used to derive the complementary functionals for the five-field, four-field, three-field, two-field and one-field variational principles more simply and directly. Furthermore, with this approach, it is possible not only to derive the variational principles given by Herrera and Bielak, Oden and Reddy, but also to develop new more general variational principles. And the intrinsic relationship among various principles can be explained clearly.     

GURTIN-TYPE REGION-WISE VARIATIONAL PRINCIPLES FOR THERMOPIEZOELECTRIC ELASTODYNAMICS

IntroductionThemethodofconvolution[1- 3]canbeusedinthestudyofpiezoelectricmaterial.Piezoelectricmaterialisoneoftheimportantsmartmaterials,usedinnovelsmartstructure .ThedynamictheoryforthermopiezoelectricelastomediawassearchedbyNowacki[4 ,5 ],Chandrasekharaiah[6 ]andIesan[7].However,region_wisevariationalprinciplesinlinearthermopiezoelectricelastodynamicshavebeennotestablishedsystematically .AlthoughLuoenandKuangJun_shang[8]havedevelopedsimplifiedGurtin_typevariationalprinciplesinlinearther…     

some general theorems and generalized and piecewise generalized variational principles for linear elastodynamics

From the concept of four-dimensional space and under the four kinds of time limit conditions, some general theorems for elastodynamics are developed, such as the principle of possible work action, the virtual displacement principle, the virtual stress-momentum principle, the reciprocal theorems and the related theorems of time terminal conditions derived from it. The variational principles of potential energy action and complementary energy action, the H-W principles, the H-R principles and the constitutive variational principles for elastodynamics are obtained. Hamilton's principle, Toupin's work and the formulations of Ref. [5], [17]-[24] may be regarded as some special cases of the general principles given in the paper. By considering three cases: piecewise space-time domain, piecewise space domain, piecewise time domain, the piecewise variational principles including the potential, the complementary and the mixed energy action fashions are given. Finally, the general formulation of piecewise variati     

The applications of generalized variational principles in nonlinear structural analysis

This paper discusses the generalized variational principles founded by thetechnique of Lagrangian multipliers in structural mechanics and analyzes the nonlinearstatically indeterminate structures.It is assumed that the stress-strain relationship ofthe materials of structures has the form ofσ=Bε~(1/m)orτ=Cγ~(1/m),namely,thephysical equations of structures have the shape of exponential functions.Severalexamples are given to illustrate the statically indeterminate structures such as thetrusses,beams,frames and torsional bars.     

电磁弹性动力学初边值问题12类变量广义变分原理

基于Yao建立的电磁弹性固体广义变分原理,运用关于非传统Hamilton型广义变分原理的方法,建立了电磁弹性动力学初边值问题的12类变量广义变分原理,可反映该问题的全部特征,其独立变分变量为该问题的全部变量,即位移、速度、动量、应变、应力、电位移、磁感应强度、电场强度、磁场强度、电标量势、磁标量势和磁矢量势.本文建立的...     

有限变形弹性动力学的非传统简化Gurtin型变分原理--文献[1]的续篇

根据古典阴阳互补和现代对偶互补的基本思想,通过作者提出的一条简单而统一的新途径,建立了有限变形弹性动力学的另一种单卷积形式的变分原理-各类非传统简化Gurtin型变分原理. 首先给出一个以卷积表示的关系式,在力学上它是有限变形动力学的广义虚功原理的另一种表式.然后从该式出发,不仅能得到有限变形动力学另一种形式的虚功原理,而且通过文中所给出的一系列广义Legendre变换,还能成对导出5类变量、3类变量、2类变量和1类变量非传统简化Gurtin型变分原理的互补泛函. 同时,通过这条新途径还能阐明这些原理之间的内在联系.     

THE MATHEMATICAL MODELS AND GENERALIZED VARIATIONAL PRINCIPLES OF NONLINEAR ANALYSIS FOR PERFORATED THIN PLATES

ＴＨＥＭＡＴＨＥＭＡＴＩＣＡＬＭＯＤＥＬＳＡＮＤＧＥＮＥＲＡＬＩＺＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＳＯＦＮＯＮＬＩＮＥＡＲＡＮＡＬＹＳＩＳＦＯＲＰＥＲＦＯＲＡＴＥＤＴＨＩＮＰＬＡＴＥＳＣｈｅｎｇＣｈａｎｇｉｕｎ（程昌钧）；ＹａｎｇＸｉａｏ...     

Generalized variational principles for boundary value problem of electromagnetic field in electrodynamics

An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given. Using Chien＇s method, a pair of generalized variational principles （GVPs） are established, which directly leads to all four Maxwell＇s equations, two intensity-potential equations, two constitutive equations, and eight boundary conditions. A family of constrained variational principles is derived sequentially. As additional verifications, two degenerated forms are obtained, equivalent to two known variational principles. Two modified GVPs are given to provide the hybrid finite element models for the present problem.